Course Topics

The course outline given below summarizes the present status of our course development. It is close to the final definition of the course, but continues to evolve as different instructors teach the material. Since we teach on a quarter schedule, the topic list could be expanded somewhat for a semester course, or more time could be devoted in the areas of recursive filters, z-transforms and frequency response. These are the vital theoretical methods that must be taken into a later course on Fourier analysis.

• Definitions of a signals and systems.
• Introduce a powerful software tool: MATLAB in our case. Assume students have enough programming experience to absorb MATLAB syntax on the fly.
• Review of some relevant mathematics: vector/matrix notation, complex numbers.
• Sinusoidal signals: amplitude, phase and frequency.
• Representing sinusoids with phasors.
• Synthesizing sounds with sums of sinusoids.
• Frequency content: combining sinusoids; harmonics, AM and FM signals.
• Sampling, aliasing and quantization.
• Filtering: the concept of smoothing data.
• Block level description of systems.
• FIR Filtering: generalize weighted averaging filters.
• Recursive Filtering: difference equations with feedback terms.
• Frequency response of simple filters: magnitude and phase response.
• Simulation of dynamic response in time domain; impulse response.
• z-transform analysis with polynomials.
• Synthesizing sounds via narrowband recursive filters.
• Spectrum analysis & spectrograms (for semester long courses).

• Textbook